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knee region prior to reaching the stress at the yield point, but once in the above-theknee region, it requires only a small increment in load to produce a sufficiently large increase in deflection to reach the yield point. Thus the corresponding yield load may be used as an adequate approximation of the buckling load for a slender column as well. Hence the yield strength provides an adequate design bound for both massive and slender columns. It is also important to note that, in general, columns found in applications are sufficiently massive that the linear theory developed here is valid within the range of deflection that is of interest. Application of Eq. (30.1) to a simply supported imperfect column with constant properties over its length yields a modification of Eq. (30.4). Thus, d2y + k2y = k2 (e Y) dx2 (30.17)

insert Inventory(EquipmentId, StatusId, LocationId, LeaseId,

Waste Group Agriculture x1 = # employees 0.83 122.06 4.23 7.14x1 3.49x2 140.4x3 + 371.10 2.18 0.86 0.79 0.84 71.48 31.50 749.43 0.84 0.80 21.10 0.43x1 0.94 3.54x1 + 11.81 0.25x1 + 35.68 0.51x1 + 6.48 0.000

where e = eccentricity of the axial load P (taken as positive in the positive y direction) and Y = initial deflection (crookedness) of the unloaded column. The x axis is taken through the end points of the centroidal axis, so that Eq. (30.5) still holds and Y is zero at the end points. Note that the functions in the right side of Eq. (30.8) form a basis for a trigonometric (Fourier) series, so that any function of interest may be expressed in terms of such a series. Thus we can write Y= where c(n) = 2 L

LeaseScheduleId, OwnerId,

n = 1

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Number of Companies Indicators x1 = # employees 13 Regression Model 1.29x1 0.27 t Statistic t Critical P Value Partial R 2 R2 0.79 F F Statistic Critical P Value 41.38 4.75 0.000

(30.18)

Lease, values ( @intStatusId, @mnyLease, Select @intErrorCode = @@Error,

(30.19)

x1 = # employees x2 = disposal $/ton x3 = ISO14001cert. x1 = 0.51 x2 = 0.14 x3 = 0.19 3.49 3.92 4.35 5.59

n = 1

AcquisitionTypeID) @intLeaseId, @intAcquisitionTypeID)

c(n)

@intEquipmentId, @intLocationId, @intLeaseScheduleId,@intOwnerId,

sin (n x/L) [EI(n /L)2 P]

0.000 0.000 0.000 0.000

(30.20)

You can integrate transaction processing perfectly with this solution. Review 5 to remind yourself why Rollback and Commit must be treated differently. At the beginning of a stored procedure or transaction, the developer should add the following code:

The maximum deflection ymax of a simply supported column will usually (except for cases with a pronounced and asymmetrical initial deformation or antisymmetrical load eccentricity) occur at the column midpoint. A good approximation (probably within 10 percent) of ymax in the above-the-knee region that may be used in deflectionlimited column design is given by the coefficient of the first term in Eq. (30.20): ymax = P[c(1) (4e/ )] EI( /L)2 P (30.21)

Food manufacturers 2.57 x1 = # employees x1 = # employees x1 = # employees 0.98x1 + 21.64 2.01x1 + 4.05 2.71x1 + 8.27

The maximum bending moment will also usually occur at the column midpoint and at incipient yielding is closely approximated by Mmax = P e Ymid + P 4e c(1) [EI( /L)2 P] (30.22)

Declare @intTransactionCountOnEntry int If @intErrorCode = 0 Begin Select @intTransactionCountOnEntry = @@TranCount BEGIN TRANSACTION End

The immediately preceding analysis deals with the bending moment about the z axis (normal to the paper). Clearly, a similar analysis can be made with regard to bending about the y axis (Fig. 30.1). Unlike the analysis of the perfect column, where it is merely a matter of finding the buckling load about the weaker axis, in the

12.35 29.84 22.39 47.11

At the end of the procedure (and/or transaction), the developer should complete the transaction:

Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.

present approach the effects about the two axes interact in a manner familiar from analysis of an eccentrically loaded short strut. We now use the familiar expression for combining direct axial stresses and bending stresses about two perpendicular axes. Since there is no ambiguity, we will suppress the negative sign associated with compressive stress: = P M(z)c(y) M(y)c(z) + + I(z) I(y) A (30.23)

5.79 5.32 5.99 4.67

If @@TranCount > @intTransactionCountOnEntry Begin If @intErrorCode = 0 COMMIT TRANSACTION Else ROLLBACK TRANSACTION End

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